Linear Difference Equation

A difference equation defined over a set A is linear over A if it can be written in the form

f0 (h)yh+n + f1 (h)yh+n-1 +?+ fn (h)yn = g(h)

where each of f0, f1, …, fn–1, fn, and g is a function of h (but not of yh) defined for all values of h in the set A. The equations (8), (9) and (10) are examples of such equations. Also we observe that the coefficients in equations (8) and (9) are constants i.e., they do not depend upon h. The equations of this type come under the category of linear difference equations with constant coefficients. The equation (10) is a linear difference equation with variable coefficients.

which is called the homogeneous linear difference equation corresponding to the equation

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